# Sum of all subsets of a set formed by first n natural numbers

Given a number n, we need to find the sum of all the elements from all possible subsets of a set formed by first n natural numbers.**Examples :**

Input : n = 2 Output : 6 Possible subsets are {{1}, {2}, {1, 2}}. Sum of elements in subsets is 1 + 2 + 1 + 2 = 6 Input : n = 3 Output : 24 Possible subsets are {{1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} Sum of subsets is : 1 + 2 + 3 + (1 + 2) + (1 + 3) + (2 + 3) + (1 + 2 + 3)

A **simple solution** is to generate all subsets. For every subset, compute its sum and finally return overall sum.

An **efficient solution** is based on the fact that every number from 1 to n appears exactly 2^{(n-1)} times. So our required sum is (1 + 2 + 3 + ..+ n) * 2^{(n-1)}. The sum can be written as (n * (n + 1)/2) * 2^{(n-1)}

## C++

`// CPP program to find sum of all subsets` `// of a set.` `#include <bits/stdc++.h>` `using` `namespace` `std;` `unsigned ` `long` `long` `findSumSubsets(` `int` `n)` `{` ` ` `// sum of subsets is (n * (n + 1) / 2) *` ` ` `// pow(2, n-1)` ` ` `return` `(n * (n + 1) / 2) * (1 << (n - 1));` `}` `int` `main()` `{` ` ` `int` `n = 3;` ` ` `cout << findSumSubsets(n);` ` ` `return` `0;` `}` |

## Java

`// Java program to find sum of all subsets` `// of a set.` `class` `GFG {` ` ` `static` `long` `findSumSubsets(` `int` `n)` ` ` `{` ` ` `// sum of subsets is (n * (n + 1) / 2) *` ` ` `// pow(2, n-1)` ` ` `return` `(n * (n + ` `1` `) / ` `2` `) * (` `1` `<< (n - ` `1` `));` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `n = ` `3` `;` ` ` `System.out.print(findSumSubsets(n));` ` ` `}` `}` `// This code is contributed by Anant Agarwal.` |

## Python3

`# Python program to find` `# sum of all subsets` `# of a set.` `def` `findSumSubsets( n):` ` ` `# sum of subsets ` ` ` `# is (n * (n + 1) / 2) *` ` ` `# pow(2, n-1)` ` ` `return` `(n ` `*` `(n ` `+` `1` `) ` `/` `2` `) ` `*` `(` `1` `<< (n ` `-` `1` `))` ` ` `# Driver code ` `n ` `=` `3` `print` `(findSumSubsets(n))` `# This code is contributed ` `# by sunnysingh.` |

## C#

`// C# program to find sum of all subsets` `// of a set.` `using` `System;` `class` `GFG {` ` ` `static` `long` `findSumSubsets(` `int` `n)` ` ` `{` ` ` `// sum of subsets is (n * (n + 1) / 2) *` ` ` `// pow(2, n-1)` ` ` `return` `(n * (n + 1) / 2) * (1 << (n - 1));` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `n = 3;` ` ` `Console.WriteLine(findSumSubsets(n));` ` ` `}` `}` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// PHP program to find sum ` `// of all subsets of a set` `function` `findSumSubsets(` `$n` `)` `{` ` ` `// sum of subsets is (n *` ` ` `// (n + 1) / 2) * pow(2, n-1)` ` ` `return` `(` `$n` `* (` `$n` `+ 1) / 2) * ` ` ` `(1 << (` `$n` `- 1));` `}` `// Driver Code` `$n` `= 3;` `echo` `findSumSubsets(` `$n` `);` `// This code is contributed by ajit` `?>` |

## Javascript

`<script>` `// javascript program to find sum of all subsets` `// of a set.` `function` `findSumSubsets( n)` `{` ` ` `// sum of subsets is (n * (n + 1) / 2) *` ` ` `// pow(2, n-1)` ` ` `return` `(n * (n + 1) / 2) * (1 << (n - 1));` `}` `// Driven Program` ` ` `let n = 3;` ` ` `document.write(findSumSubsets(n));` `// This code contributed by aashish1995` `</script>` |

**Output :**

24

**Time Complexity:** O(1)**Auxiliary Space:** O(1)

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